On the upper bounding approach to thermal convection at moderate Rayleigh numbers. 2: Rigid boundaries
Abstract
Numerical solutions for two upper bounding problems for thermal convection in a horizontal layer of fluid contained between perfectly conducting rigid boundaries are presented. Problem 1 was first introduced by Howard (1963) and yields an upper bound on the heat transport which is independent of Prandtl number. The numerical solutions of this problem indicate that this boundary layer approach overestimates this upper bound somewhat. Solutions are investigated for three horizontal wavenumbers. Problem 2, which is valid for large Prandtl number fluids, yields an upper bound on the heat transport which is smaller than that given by Problem 1. The transitions involved are discussed.
 Publication:

Interim Report Aerospace Corp
 Pub Date:
 January 1975
 Bibcode:
 1975aero.reptX....S
 Keywords:

 Convective Heat Transfer;
 Gas Dynamics;
 Hydrodynamics;
 Rayleigh Number;
 Boundary Value Problems;
 Mathematical Models;
 Numerical Analysis;
 Fluid Mechanics and Heat Transfer